{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\nRobust linear estimator fitting\n===============================\n\nHere a sine function is fit with a polynomial of order 3, for values\nclose to zero.\n\nRobust fitting is demoed in different situations:\n\n- No measurement errors, only modelling errors (fitting a sine with a\n  polynomial)\n\n- Measurement errors in X\n\n- Measurement errors in y\n\nThe median absolute deviation to non corrupt new data is used to judge\nthe quality of the prediction.\n\nWhat we can see that:\n\n- RANSAC is good for strong outliers in the y direction\n\n- TheilSen is good for small outliers, both in direction X and y, but has\n  a break point above which it performs worse than OLS.\n\n- The scores of HuberRegressor may not be compared directly to both TheilSen\n  and RANSAC because it does not attempt to completely filter the outliers\n  but lessen their effect.\n\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "from matplotlib import pyplot as plt\nimport numpy as np\n\nfrom sklearn.linear_model import (\n    LinearRegression, TheilSenRegressor, RANSACRegressor, HuberRegressor)\nfrom sklearn.metrics import mean_squared_error\nfrom sklearn.preprocessing import PolynomialFeatures\nfrom sklearn.pipeline import make_pipeline\n\nnp.random.seed(42)\n\nX = np.random.normal(size=400)\ny = np.sin(X)\n# Make sure that it X is 2D\nX = X[:, np.newaxis]\n\nX_test = np.random.normal(size=200)\ny_test = np.sin(X_test)\nX_test = X_test[:, np.newaxis]\n\ny_errors = y.copy()\ny_errors[::3] = 3\n\nX_errors = X.copy()\nX_errors[::3] = 3\n\ny_errors_large = y.copy()\ny_errors_large[::3] = 10\n\nX_errors_large = X.copy()\nX_errors_large[::3] = 10\n\nestimators = [('OLS', LinearRegression()),\n              ('Theil-Sen', TheilSenRegressor(random_state=42)),\n              ('RANSAC', RANSACRegressor(random_state=42)),\n              ('HuberRegressor', HuberRegressor())]\ncolors = {'OLS': 'turquoise', 'Theil-Sen': 'gold', 'RANSAC': 'lightgreen', 'HuberRegressor': 'black'}\nlinestyle = {'OLS': '-', 'Theil-Sen': '-.', 'RANSAC': '--', 'HuberRegressor': '--'}\nlw = 3\n\nx_plot = np.linspace(X.min(), X.max())\nfor title, this_X, this_y in [\n        ('Modeling Errors Only', X, y),\n        ('Corrupt X, Small Deviants', X_errors, y),\n        ('Corrupt y, Small Deviants', X, y_errors),\n        ('Corrupt X, Large Deviants', X_errors_large, y),\n        ('Corrupt y, Large Deviants', X, y_errors_large)]:\n    plt.figure(figsize=(5, 4))\n    plt.plot(this_X[:, 0], this_y, 'b+')\n\n    for name, estimator in estimators:\n        model = make_pipeline(PolynomialFeatures(3), estimator)\n        model.fit(this_X, this_y)\n        mse = mean_squared_error(model.predict(X_test), y_test)\n        y_plot = model.predict(x_plot[:, np.newaxis])\n        plt.plot(x_plot, y_plot, color=colors[name], linestyle=linestyle[name],\n                 linewidth=lw, label='%s: error = %.3f' % (name, mse))\n\n    legend_title = 'Error of Mean\\nAbsolute Deviation\\nto Non-corrupt Data'\n    legend = plt.legend(loc='upper right', frameon=False, title=legend_title,\n                        prop=dict(size='x-small'))\n    plt.xlim(-4, 10.2)\n    plt.ylim(-2, 10.2)\n    plt.title(title)\nplt.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.6.7"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}